Bibliographic record
Abstract
In the famous network creation game of Fabrikant et al. a set of agents play a game to build a connected graph. The $n$ agents form the vertex set $V$ of the graph and each vertex $v\in V$ buys a set $E_v$ of edges inducing a graph $G=(V,\bigcup\limits_{v\in V} E_v)$. The private objective of each vertex is to minimize the sum of its building cost (the cost of the edges it buys) plus its connection cost (the total distance from itself to every other vertex). Given a cost of $α$ for each individual edge, a long-standing conjecture, called the tree conjecture, states that if $α> n$ then every Nash equilibrium graph in the game is a spanning tree. After a plethora of work, it is known that the conjecture holds for any $α>3n-3$. In this paper we prove the tree conjecture holds for $α>2n$. This reduces by half the open range for $α$ with only $[n, 2n)$ remaining in order to settle the conjecture.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.004 | 0.005 |
| Scholarly communication | 0.005 | 0.029 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.006 | 0.010 |
| Insufficient payload (model declined to judge) | 0.019 | 0.005 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".